Scale Factor and the relationship to area and volume GLE SPI:

Remember these rules !! If 2 shapes are similar, it is by multiplication The number that we multiply by is the scale factor. Scale factor is the ratio of corresponding parts.

Let’s review, what we know about similar shapes. 2.8 cm x 5.6 cm 1.75 cm = x = 2.8 x x = 3.5 cm

Try again 6 m x 1.5 m 8 m 6 8= x = 6 x 66 x = 2 m

Remember: if shapes are similar it is because they are related by multiplication. If a shape doubles, the scale factor is 2; if the shape triples in size, the scale factor is 3, and so on.

1.75 cm 3.5 cm 2.8 cm 5.6 cm The second quadrilateral is twice as tall and twice as wide. This means the scale factor is 2.

Scale factor and Area

1.75 cm 3.5 cm 2.8 cm 5.6 cm The rule: to find the area of the second shape multiply the area of the first times the scale factor squared. The scale factor is 2, so its square is 4… let’s test it.

1.75 cm 3.5 cm 2.8 cm 5.6 cm Since the scale factor is 2, the shape is twice as tall and twice as wide. ( l * w) scale factor x 2.8 x x 2.8 x 4 = 19.6 cm 2 Check yourself.. is that = to 5.6 x 3.5 ? Remember, you are using the scale factor to find area when you don’t know the length of all the sides.

The second tripled in size, so the scale factor is The area of the second: Area of first x 10 x x 9 = 90 Is this true if you use the formula ½ b x h 2 Yes, ½ 15 * 12 = 90

The reason this works is because area is increased by length and width. If both dimensions are increased, you are square – ing.

6m 18m 2m The second shape is 3x as big, so the scale factor is 3. The area of the first times the Scale factor x 3 2 = 12 x 9 = 108m 2

10 cm If the scale factor is ½ what would be the area of the smaller? Area of the first times the scale factor 2 10 * 10 * ( 1 / 2 ) 2= 100 * ¼ = 25 cm 2

Scale factor and volume

Now let’s look at scale factor and volume. The rule is to multiply the volume of the known times the scale factor 3. Remember you are increasing the length, width, and height of a shape, thus cube - ing.

10 cm 3 cm 5 cm 30 cm The scale factor is 3, because the size has tripled. What is the volume of the larger prism? Hint: volume of small x scale factor x 3 3 =150 x 27 = 4050 cm 3

10 m 5 m 30 m What is the scale factor? Hint: volume of small x scale factor x (1/2) 3 =750 x 1/8 = cm 3 ½ the shape is reduced by 2 What is the volume of the small?

Now Check yourself !! lengthwidthScale factor /2 Answers:

Now Check yourself !! Answers: lengthwidthheightScale factor /5 Assume all the shapes are cubes